Math 170B: General Course Outline
Catalog Description
    170B. Probability Theory. (4) Lecture, three hours; discussion, one hour. Requisite: course 170A or Statistics 100A. Convergence in distribution, normal approximation, laws of large numbers, Poisson processes, random walks. P/NP or letter grading.
Textbook
    Sheldon Ross, 7th Ed.
Reviews & Exams
    The following scheduleis for 26 lectures. The remaining classi room meetings are for leeway and one or two midterm exams. For lectures marked with "*" see the comments below.
Schedule of Lectures

Lecture
Section
Topics and Example Numbers
.
.
Sums of random variables
1
6.1,6.2,6.7
Review of basics
2
6.3
Sum of independent random variables
3
7.2
Expectation of sums
4-5
7.4
Variance of sums, covariance and correlations
.
.
The use of indicators
6
7.3
Moments of the number of events that occur
7
1.5,6.1(1f),7.4(4f)
Multinomial coefficients, multinomial random variables
8
4.8.3,7.2(2g),7.3(3b)
Hypergeometric random variables
9
2.5(5m),3.5(5d),7.2(2h),7.3(3c)
The match problem.
.
.
Conditional distribution
10
6.4,6.5
Conditional distribution: discrete / continuous case
11-12
7.5
Conditional expectation and variance
.
.
Moment Generating Functions
13*
7.6
Conditional expectation and prediction
14-15
7.7
Moment generating and joint moment generating function
16
7.8.1
Multivariate normal distribution
17
7.8.2,7.3(after 3b)
Sample mean and variance, chi-squared distribution
.
.
Limit theorems
18
8.2
Chebyshev's inequality, weak law of large numbers
19-20
8.3
Central limit theorem, normal approximation
21*
8.5
Other Inequalities
22*
8.6
Poisson approximation
.
.
Stochastic processes
23
9.1
The Poisson process
24-26*
3.4(4k)
Random walks: gambler's ruin problem, reflection principle, arcsine law, recurrence/transience, oscillations

Comments

Apart from the gambler's ruin problem, random walks are not covered in Ross. A possible source for additional material for lectures 24-26 is Stirzaker (5.6,6.8), or Feller.

If time is too short the easiest thing to do is to skip one or more of the lectures 13, 21, 22.

Outline update: T. Richthammer, 8/08
For more information, please contact Student Services, ugrad@math.ucla.edu.
 

UCLA Department of Mathematics                          Search     Home